Question

What is the relationship between the bandwidth and the Q-factor in a resonant circuit?

• A. $Q = BW$
• B. $Q = \dfrac{f_0}{BW}$
• C. $Q = BW^2$
• D. $Q = \dfrac{BW}{f_0}$

Hint:

Q-factor ↑ → Bandwidth ↓ → $Q = \dfrac{f_0}{BW}$.

Answer 1

The Correct Option is B

Concept: In a resonant circuit, the Quality factor (Q-factor) indicates how sharp or selective the resonance is. It relates the resonant frequency to the bandwidth.
Step 1: Understanding Q-factor.
Q-factor is defined as the ratio of resonant frequency ($f_0$) to the bandwidth (BW).
Step 2: Mathematical relation.
\[ Q = \frac{f_0}{BW} \]
Step 3: Interpretation.

• High Q → Narrow bandwidth → Sharp resonance
• Low Q → Wide bandwidth → Broad response

Step 4: Conclusion.
Thus, Q-factor is inversely proportional to bandwidth.